592 CHAPTER 15 NONPARAMETRIC STATISTICSEXERCISES FOR SECTION 15-5
15-37. Montgomery (2001) presented the results of an ex-
periment to compare four different mixing techniques on the
tensile strength of portland cement. The results are shown in
the following table. Is there any indication that mixing tech-
nique affects the strength? Use 0.05.Mixing
Technique Tensile Strength (lb/in.^2 )
1 3129 3000 2865 2890
2 3200 3000 2975 3150
3 2800 2900 2985 3050
4 2600 2700 2600 276515-38. An article in the Quality Control Handbook, 3rd edi-
tion (McGraw-Hill, 1962) presents the results of an experiment
performed to investigate the effect of three different conditioning
methods on the breaking strength of cement briquettes. The data
are shown in the following table. Using 0.05, is there any
indication that conditioning method affects breaking strength?Conditioning
Method Breaking Strength (lb/in.^2 )
1 553 550 568 541 537
2 553 599 579 545 540
3 492 530 528 510 57115-39. In Statistics for Research(John Wiley & Sons,
1983), S. Dowdy and S. Wearden presented the results of an
experiment to measure the performance of hand-held chain
saws. The experimenters measured the kickback angle
through which the saw is deflected when it begins to cut a
3-inch stock synthetic board. Shown in the following table aredeflection angles for five saws chosen at random from each of
four different manufacturers. Is there any evidence that the
manufacturers’products differ with respect to kickback angle?
Use 0.01.Manufacturer Kickback Angle
A 42 17 24 39 43
B 28 50 44 32 61
C 57 45 48 41 54
D 29 40 22 34 3015-40. Consider the data in Exercise 13-2. Use the
Kruskal-Wallis procedure with 0.05 to test for differ-
ences between mean uniformity at the three different gas flow
rates.
15-41. Find the approximate P-value for the test statistic
computed in Exercise 15-37.
15-42. Find the approximate P-value for the test statistic
computed in Exercise 15-40.Supplemental Exercises15-43. The surface finish of 10 metal parts produced in a
grinding process is as follows: (in microinches): 10.32, 9.68,
9.92, 10.10, 10.20, 9.87, 10.14, 9.74, 9.80, 10.26. Do the data
support the claim that the median value of surface finish is 10
microinches? Use the sign test with 0.05. What is the
P-value for this test?
15-44. Use the normal appoximation for the sign test for
the problem in Exercise 15-43. Find the P-value for this test.
What are your conclusions if 0.05?
15-45. Fluoride emissions (in ppm) from a chemical plant
are monitored routinely. The following are 15 observationsthe Kruskal-Wallis test is approximately equivalent to applying the usual analysis of variance
to the ranks.
The rank transformation has wide applicability in experimental design problems for which
no nonparametric alternative to the analysis of variance exists. If the data are ranked and the or-
dinary F-test is applied, an approximate procedure results, but one that has good statistical
properties. When we are concerned about the normality assumption or the effect of outliers or
“wild” values, we recommend that the usual analysis of variance be performed on both the
original data and the ranks. When both procedures give similar results, the analysis of variance
assumptions are probably satisfied reasonably well, and the standard analysis is satisfactory.
When the two procedures differ, the rank transformation should be preferred since it is less
likely to be distorted by nonnormality and unusual observations. In such cases, the experi-
menter may want to investigate the use of transformations for nonnormality and examine the
data and the experimental procedure to determine whether outliers are present and why they
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